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26 January 2014 @ 12:17 pm
Thing that I learned yesterday (one among many, but this is the most memorable):  
The first derivative of distance related to time (change in distance over time) (dx/dt) is velocity.

The second derivative (change in velocity over time) (d2x/dt2) is acceleration.

The third derivative (change in acceleration over time) (d3x/dt3) is jerk.

I knew all of those.

The fourth derivative is jounce.

The fifth, sixth, and seventh derivatives are snap, crackle, and pop.

This makes me very happy.
 
 
Tom the Alien Cat: arresting tomtac on January 27th, 2014 01:27 pm (UTC)
Thanks for posting this. Just this past weekend, I was throwing together a simulation of the first three, but accidentally put in a fourth and now have a simulation of jerk-acc-vel and position.

I have been using a program like that for decade, and always thought of jerk-jounce and snap as what happens to the throttle of a rocket engine. (But did not know the names.)

So "constant jerk" is where one advances the throttle at a constant rate, so the acceleration gets stronger and stronger as it builds. (My program only allows increments and decrements of one.) The astronaut might first feel just 2G, then it can build to much higher. "Jounce" could be the pressure one puts on the moving throttle to get it to move faster toward full throttle or back to zero throttle or reverse.

And, by the way, an example of positive jerk is what happens when the rocket thrust is constant, but mass of the rocket gets smaller as the fuel is used up -- the acceleration increases. And that is usually a "non-constant jerk". So this is a practical example of jounce.
Janet Miles, CAP-OMjanetmiles on January 27th, 2014 01:49 pm (UTC)
Thank you! That's very cool.